Answered

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An angle measures 24.6° more than the measure of its complementary angle. What is the measure of each angle? _and_

Sagot :

You have two angles, let's call them ∠1 and ∠2 of unknown measure, one of them measures 24.6º more than the other and both angles are complementary.

Let "xº" be the measure of ∠1, then ∠2 will beasure (x+24.6)º

∠1 and ∠2 are complementar, this means that together they add up to 90º

[tex]\angle1+\angle2=90º[/tex]

Replace the expression with the angles measures

[tex]x+(x+24.6)=90[/tex]

And solve for x

[tex]\begin{gathered} 2x+24.6=90 \\ 2x=90-24.6 \\ 2x=63.6 \\ \frac{2x}{2}=\frac{65.4}{2} \\ x=32.7 \end{gathered}[/tex]

The angles measure:

∠1=32.7º

∠2=32.7+24.6=57.3º

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